Estimating the smoothing parameter in generalized spline-based regression: II. Empirical and fully Bayesian approaches. Experiences with Gibbs sampling in simulated results
type: Item
instance of: scholarly article
title: Estimating the smoothing parameter in generalized spline-based regression: II. Empirical and fully Bayesian approaches. Experiences with Gibbs sampling in simulated results
zbMATH Open document ID: 1007.62037
published in: Computational Statistics
publication date: 2003-03-09T00:00:00Z
review text: [For part I of this paper see the preceding entry, Zbl 1007.62036] A nonparametric regression model is considered with binary or Gaussian responses where the expectation of the data is a smooth function of the covariates. A spline technique is used for estimation of this function. The author interprets the standard cross-validation approach for choice of the smoothing parameter as an empirical Bayes one and develops a fully Bayesian approach based on an improper prior \(p(h/\gamma^2)\propto\exp(-\gamma^{-2}J(h))\) on the space of possible regression functions \(h\), where \(J\) is a roughness penalty and the smoothing parameter \(\gamma^{-2}\) is considered as a hyperparameter. In the examples the distribution of \(\gamma^{-2}\) is taken as Gamma or Pareto. Results of simulations are presented for quadratic and quadratic \(+\) sinusoidal functions \(h\).
Mathematics Subject Classification ID: 62G08
Mathematics Subject Classification ID: 62C12
Mathematics Subject Classification ID: 62-08
Mathematics Subject Classification ID: 62F15
zbMATH DE Number: 1878600
zbMATH Keywords: Markov chain Monte Carlo
zbMATH Keywords: spline smoothing
zbMATH Keywords: empirical Bayes
author: Angelika van der Linde
MaRDI profile type: Publication
full work available at URL: s001800100052
OpenAlex ID: W3180051445
DOI: 10.1007/S001800100052
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description: scientific article; zbMATH DE number 1878600